Adaptive Dynamic Surface Control Research Articles

Neural network controller design for fractional-order systems with input nonlinearities and asymmetric time-varying Pseudo-state constraints

Abstract This article considers the neural adaptive control issues of a category of non-integer-order non-square plants with actuator Nonlinearities and Asymmetric Time-Varying pseudo-State Constraints. First, the original non-square non-affine system with input nonlinearities is transformed into an equivalent affine-in-control square model by defining a set of auxiliary variables and by employing the mean-value theorem. Second, Neural networks and Nussbaum functions are exploited to obviate the requirement of a complete knowledge of the system dynamics and the control directions, respectively. Third, a novel adaptive dynamic surface control method based on Caputo fractional derivative definitions and fractional order filters is developed to overcome the “explosion of complexity” problem in the traditional backstepping design process and to determine the parameter update laws and control signals, concurrently. Then, Asymmetric Barrier Lyapunov Functions with error variables are adopted to ensure the uniform stability of the closed-loop system and to prevent the violation of the full pseudo-State constraints. The novelties and contributions of this article are: (1) through the introduction of new technical Lemmas and corollaries, existing control design and stability theories linked to integer-order square systems are developed and extended to non-square non-integer-order ones. (2) all signals, including variables and errors in the closed-loop system are semi-global practical finite-time stability whereas the the tracking errors are asymptotically driven to zero without transgression of the constraints. Finally, the effectiveness and potential of the proposed control approach are substantiated by two example simulations.

The Set-Invariance Paradigm in Fuzzy Adaptive DSC Design of Large-Scale Nonlinear Input-Constrained Systems

This paper proposes a novel set-invariance adaptive dynamic surface control (DSC) design for a larger class of uncertain large-scale nonlinear input-saturated systems. The peculiarity of this class is that no <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> bound on the continuous control gain functions is assumed (i.e., their boundedness cannot be assumed before obtaining system stability). This requires a new design. Differently from the available methods, the proposed design involves the construction of appropriate invariant sets for the closed-loop trajectories, which allows to remove the restrictive assumption of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> bounds of the control gain functions. Furthermore, we show that such set-invariance design can handle input constraints in the form of input saturation. In line with the DSC methodology, semi-globally uniformly ultimate boundedness is proven: however, differently from the standard methodology, stability analysis requires the combination of Lyapunov and invariant set theories.

Adaptive Pseudo Inverse Control for a Class of Nonlinear Asymmetric and Saturated Nonlinear Hysteretic Systems

This paper aims at eliminating the asymmetric and saturated hysteresis nonlinearities by designing hysteresis pseudo inverse compensator and robust adaptive dynamic surface control (DSC) scheme. The “pseudo inverse” means that an on-line calculation mechanism of approximate control signal is developed by applying a searching method to the designed temporary control signal where the true control signal is included. The main contributions are summarized as: 1) to our best knowledge, it is the first time to compensate the asymmetric and saturated hysteresis by using hysteresis pseudo inverse compensator because the construction of the true saturated-type hysteresis inverse model is very difficult; 2) by designing the saturated-type hysteresis pseudo inverse compensator, the construction of true explicit hysteresis inverse and the identifications of its corresponding unknown parameters are not required when dealing with the saturated-type hysteresis; 3) by combining DSC technique with the tracking error transformed function, the “explosion of complexity” problem in backstepping method is overcome and the prespecified tracking performance is achieved. Analysis of stability and experimental results on the hardware-in-loop platform illustrate the effectiveness of the proposed adaptive pseudo inverse control scheme.

Observer-based dynamic surface control for flexible-joint manipulator system with input saturation and unknown disturbance using type-2 fuzzy neural network

In this paper, the nonlinear disturbance observer (NDO) based dynamic surface control (DSC) with interval type-2 fuzzy neural network (IT2FNN) approximator is proposed for flexible-joint manipulator with the input saturation and unknown nonlinear disturbance. The DSC technique has tremendous advantages in eliminating the ’explosion of complexity’ problem. The IT2FNN approximator is used to deal with parameter uncertainties. The NDO is applied to estimate the unknown external disturbance and compensate the saturation constrain. From Lyapunov stability analysis, it is proved that with the proposed control scheme, all signals of the closed-loop system are semiglobally uniformly ultimately bounded. Simulation results are carried out to demonstrate the effectiveness of the proposed scheme. Compared with the adaptive DSC with neural network (NN) approximator and type-1 fuzzy (T1F) approximator, the tracking error of the proposed control scheme converges to a sufficiently small value.

Robust adaptive multistage anti-windup dynamic surface control for dynamic positioning ships with mismatched disturbance

In this paper, a novel robust adaptive multistage anti-windup control strategy is developed for dynamic positioning ships in presence of input constraint, mismatched disturbance and external disturbance. Based on dynamic surface control technique, a composite control law, where both mismatched and matched disturbances are compensated, is established to stabilize the system without the requirement of solving any partial differential equations. In particularly, the mismatched disturbance caused by the model transformation is analyzed firstly and the better steady performance is achieved. In addition, a novel multistage anti-windup control based on anticipatory activation compensation is constructed to handle the input constraint while the transient performance is improved significantly. Moreover, the stability of the closed-loop system is proven via Lyapunov technique rigorously, and the tracking error can be forced into an arbitrarily small neighborhood around zero. Finally, simulations with comparisons demonstrate the effectiveness of the proposed method.

Full-State Constrained Adaptive Fuzzy Finite-Time Dynamic Surface Control for PMSM Drive Systems

This paper proposes an adaptive fuzzy finite-time dynamic surface control method for permanent magnet synchronous motors (PMSMs) with full-state constraints. By combining with the finite-time stability theory, the $$\log $$ -type barrier Lyapunov function is constructed to constrain the angular speed, stator current and other state variables of PMSMs in the predefined compact sets. Then, the first-order filter is employed to solve the shortcoming of “complexity of differentiation” in backstepping approach and the fuzzy logic systems are used to approximate the nonlinear functions. Finally, it is demonstrated that the presented control approach realizes fast tracking effect and the boundedness of all signals. Comparison of simulation results is included to illustrate the superiority of the new design scheme.

Adaptive Dynamic Surface Control for a Class of Dead-Zone Nonlinear Systems via Output Feedback

The paper aims to address output feedback problem for a class of nonlinear systems subjected to unknown dead-zone. High-gain K-filters is firstly designed such that unavailable states of system can be reconstructed. Then, with the help of dynamic surface control (DSC) method, an adaptive output feedback controller design is established, which can alleviate undesired influence of the dead-zone and guarantee the semi-global stability of the system. Furthermore, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {L_{\infty }}$ </tex-math></inline-formula> performance of tracking error is achieved by means of initialization technique. Ultimately, numerical and practical examples clarify the efficiency of the proposed solution.

Attitude Tracking Control of Small-Scale Unmanned Helicopters Using Quaternion-Based Adaptive Dynamic Surface Control

In this paper, a quaternion-based adaptive dynamic surface control method is proposed for attitude tracking control for small-scale unmanned helicopters with external disturbance and uncertain dynamics. The quaternion formalism is introduced and a quaternion-based multi-input-multi-output nonlinear model is derived from the attitude dynamics of a small-scale helicopter. The low-complexity controllers are designed by the dynamic surface control method as it eliminates the problem of the explosion of items. The singularity problem is avoided by substituting Euler kinematic equations in the nonlinear model with quaternion expressions and integrating the quaternion expressions into the design process of the dynamic surface control. For improving the robustness of the control system, the radial basis function networks are applied to approximate the uncertain dynamics. The external disturbance is also compensated in the controllers’ design. This paper proves that the proposed method can guarantee the uniformly ultimate boundness of this attitude system. Simulation results are presented finally and show the effectiveness of this control approach.

Antidisturbance Control for AUV Trajectory Tracking Based on Fuzzy Adaptive Extended State Observer.

In this paper, an output-feedback fuzzy adaptive dynamic surface controller (FADSC) based on fuzzy adaptive extended state observer (FAESO) is proposed for autonomous underwater vehicle (AUV) systems in the presence of external disturbances, parameter uncertainties, measurement noises and actuator faults. The fuzzy logic system is incorporated into both the observers and controllers to improve the adaptability of the entire system. The dynamics of the AUV system is established first, considering the external disturbances and parameter uncertainties. Based on the dynamic models, the ESO, combined with a fuzzy logic system tuning the observer bandwidth, is developed to not only adaptively estimate both system states and the lumped disturbances for the controller, but also reduce the impact of measurement noises. Then, the DSC, together with fuzzy logic system tuning the time constant of the low-pass filter, is designed using estimations from the FAESO for the AUV system. The asymptotic stability of the entire system is analyzed through Lyapunov’s direct method in the time domain. Comparative simulations are implemented to verify the effectiveness and advantages of the proposed method compared with other observers and controllers considering external disturbances, parameter uncertainties and measurement noises and even the actuator faults that are not considered in the design process. The results show that the proposed method outperforms others in terms of tracking accuracy, robustness and energy consumption.

Finite‐time adaptive neural dynamic surface control for non‐linear systems with unknown dead zone

Finite‐time adaptive neural dynamic surface control for non‐linear systems with unknown dead zone

Adaptive Dynamic Surface Control of a Flexible Robot Based on the K-State Observer

Adaptive Dynamic Surface Control of a Flexible Robot Based on the K-State Observer

Fuzzy adaptive dynamic surface control for strict-feedback nonlinear systems with unknown control gain functions

In this work, the fuzzy adaptive output feedback control is investigated for single-input single-output (SISO) uncertain nonlinear systems in strict-feedback form. The controlled systems under consideration of this work contain the immeasurable states and unknown control gain functions. The immeasurable states are estimated by constructing a fuzzy state observer, and the uncertain nonlinear functions are approximated by fuzzy logic systems. In order to settle the issue of ‘explosion of complexity’ inherent in the conventional backstepping design process, the ‘dynamic surface control’ (DSC) method is introduced. An observer-based fuzzy adaptive control algorithm is proposed by employing the adaptive backstepping control design technique and constructing the Logarithm Lyapunov functions. The designed fuzzy adaptive control scheme can settle the complexity problem of control scheme and insure that the closed-loop system is semi-globally uniformly ultimately boundedness (SGUUB), a simulation example is considered to illustrate the availability of the designed controller.

Adaptive Neural Dynamic Surface Control for the Chaotic PMSM System with External Disturbances and Constrained Output

Background:This article studies the issue of adaptive neural dynamic surface control for the chaotic permanent magnet synchronous motor system with constrained output, external disturbances and parameter perturbations.Methods:Firstly, a virtual controller and two practical controllers are created based on the backstepping framework. In the process of creating controllers, adaptive technique and radial basis function neural networks are used to handle unknown parameters and nonlinearities, respectively. The nonlinear damping items are applied to overcome external disturbances. The barrier Lyapunov function is used to prevent the violation of system output constraint. Meanwhile, the first-order filter to eliminate the “explosion of complexity” of traditional back stepping has been introduced. Then, it is proved that all the closed-loop signals are uniform ultimate asymptotic stability and the tracking error converges to a small set of origin.Results:The effectiveness and robustness of the developed approach are illustrated by numerical simulations.Conclusion:The raised control scheme is a useful tool for enhancing the performance of the chaotic PMSM system with external disturbances, constrained output and parameter perturbations.

Neural-Network-Based Adaptive DSC Design for Switched Fractional-Order Nonlinear Systems.

Due to the particularity of the fractional-order derivative definition, the fractional-order control design is more complicated and difficult than the integer-order control design, and it has more practical significance. Therefore, in this article, a novel adaptive switching dynamic surface control (DSC) strategy is first presented for fractional-order nonlinear systems in the nonstrict feedback form with unknown dead zones and arbitrary switchings. In order to avoid the problem of computational complexity and to continuously obtain fractional derivatives for virtual control, the fractional-order DSC technique is applied. The virtual control law, dead-zone input, and the fractional-order adaptive laws are designed based on the fractional-order Lyapunov stability criterion. By combining the universal approximation of neural networks (NNs) and the compensation technique of unknown dead-zones, and stability theory of common Lyapunov function, an adaptive switching DSC controller is developed to ensure the stability of switched fractional-order systems in the presence of unknown dead-zone and arbitrary switchings. Finally, the validity and superiority of the proposed control method are tested by applying chaos suppression of fractional power systems and a numerical example.

Adaptive Neural Network Finite-Time Dynamic Surface Control for Nonlinear Systems.

This article addresses the problem of finite-time neural network (NN) adaptive dynamic surface control (DSC) design for a class of single-input single-output (SISO) nonlinear systems. Such designs adopt NNs to approximate unknown continuous system functions. To avoid the "explosion of complexity" problem, a novel nonlinear filter is developed in control design. Under the framework of adaptive backstepping control, an NN adaptive finite-time DSC design algorithm is proposed by adopting a smooth projection operator and finite-time Lyapunov stable theory. The developed control algorithm means that the tracking error converges to a small neighborhood of origin within finite time, which further verifies that all the signals of the controlled system possess globally finite-time stability (GFTS). Finally, both numerical and practical simulation examples and comparing results are provided to elucidate the superiority and effectiveness of the proposed control algorithm.

Adaptive composite neural network disturbance observer-based dynamic surface control for electrically driven robotic manipulators

This paper presents an adaptive backstepping control scheme for electrically driven robotic manipulator (EDRM) system with uncertainties and external disturbances by using neural network disturbance observer (NNDO) and dynamic surface control (DSC) design technique. NNDO is employed to estimate the uncertainties and external disturbances such that the priori information of the unknown dynamics will not be needed. To overcome the problem of “explosion of complexity” inherent in the backstepping design method, the DSC technique is integrated into the adaptive backstepping control design framework, where the NNDOs with adaptive composite law are utilized to compensate the uncertainties and external disturbances of EDRM. Based on the Lyapunov stability theory, it can be proven that the closed-loop system is stable in the sense that all the variables are guaranteed to be uniformly ultimately bounded. The results of simulation and experimental tests demonstrate the approximation capability of NNDO and the effectiveness of the proposed adaptive DSC scheme.

Neural Adaptive Dynamic Surface Asymptotic Tracking Control for a Class of Uncertain Nonlinear System

In this paper, by incorporating the neural network into an adaptive dynamic surface control (DSC) framework, a neural adaptive DSC algorithm is developed for a class of uncertain nonlinear system to ensure the asymptotic output tracking. Neural network is used to approximate the unknown nonlinear term in the system such that the requirements for known nonlinear term in control laws design procedure are released. In order to eliminate the boundary layer effects, which are caused by the linear filters at each step in the DSC procedure, the nonlinear filters with the compensation term are designed skillfully. The proposed neural adaptive DSC algorithm not only avoids the inherent problem of “explosion of complexity” in the backstepping procedure, but also has its own advantages: (1) releasing the requirements for known nonlinear term in control laws design procedure; (2) holding the asymptotic output tracking performance. Some simulations are shown to demonstrate the effectiveness and advantages of the proposed controller.

Adaptive dynamic surface control of a class of pure feedback systems preceded by generalized P‐I hysteresis

AbstractIn this paper, an adaptive dynamic surface control is proposed for a class of completely non‐affine nonlinear systems preceded by the generalized Prandtl–Ishlinskii (P‐I) hysteresis, in which the hysteresis input function is also non‐affine with respect to the control input. Instead of the mean value theorem widely used in existing literature, new nonlinear functions are introduced, leading to the removal of the assumption caused by the mean value theorem. Moreover, no constraint is imposed on the bound of the P‐I hysteresis density function. Then, the filtered signals are constructed to address the algebraic loop problem and the complexity explosion inherent in backstepping method. Based on the filtered signals, the adaptive dynamic surface control is developed, which can ensure the transient tracking performance.

Adaptive multi-dimensional Taylor network dynamic surface control for a class of strict-feedback uncertain nonlinear systems with unmodeled dynamics and output constraint

Unmodeled dynamics and output constraint are very often experienced in many physical applications, while few studies on them simultaneously are constructed. This study concentrates on the problem of adaptive multi-dimensional Taylor network dynamic surface control (MTN-DSC) for a class of strict-feedback uncertain nonlinear systems subjected to unmodeled dynamics and output constraint. The purpose is to make this study more practical, and design a controller with simple structure to improve the system performance. A barrier Lyapunov function is used to restrict the system output to within the prescribed constraint. At each step during the backstepping design process, an MTN is applied to approach the generated unknown composite function stemming from the unknown functions and uncertain disturbances, rather than individually; this simplifies the structure and reduces the complexity of the controllers. Meanwhile, the computational burden is further reduced, as only one parameter is adjusted online, which has the minimum number of parameters to be adjusted. Additionally, DSC technique is introduced to eliminate the inherent “explosion of complexity” problem in traditional backstepping design procedure. Furthermore, it is proved that all signals of the closed-loop system are semi-globally uniformly ultimately bounded, and that the output constraint is never violated. The validity of the proposed control scheme is illustrated through the numerical and applied simulation examples.

Adaptive Neural Dynamic Surface Control With Prespecified Tracking Accuracy of Uncertain Stochastic Nonstrict-Feedback Systems.

This article addresses the adaptive neural tracking control problem for a class of uncertain stochastic nonlinear systems with nonstrict-feedback form and prespecified tracking accuracy. Some radial basis function neural networks (RBF NNs) are used to approximate the unknown continuous functions online, and the desired controller is designed via the adaptive dynamic surface control (DSC) method and the gain suppressing inequality technique. Different from the reported works on uncertain stochastic systems, by combining some non-negative switching functions and dynamic surface method with the nonlinear filter, the design difficulty is overcome, and the control performance is analyzed by employing stochastic Barbalat's lemma. Under the constructed controller, the tracking error converges to the accuracy defined a priori in probability. The simulation results are shown to verify the availability of the presented control scheme.